Data-Driven Mechanistic-Based Learning and Design of Metamaterial Systems

Metamaterials are emerging as a new paradigmatic material system to render unprecedented and tailorable properties for a wide variety of engineering applications. However, the inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space, multiple local optima, and high computational cost. To address these hurdles, we propose a data-driven metamaterial design approach that hinges on the development of three novel computational modules: (1) Collection and generation of high-quality precomputed multi-class unit cell datasets based on domain knowledge, literature, and physical simulations, (2) Creation of machine learning models to avoid costly on-the-fly physical simulations in design synthesis, and (3) Scalable ML-based TO of either unit cell or multi-scale structures. 

In this talk, we will present the methods developed for each of these three topic areas.  Specifically, we present metrics and a new efficient data acquisition method using active learning and the Determinantal Point Processes (DPP) approach, for creating unbiased, high-quality, and large multi-class dataset by optimizing the joint diversity of shape and properties.  We show a smaller yet diverse set of unit cells leads to scalable search and unbiased learning.    Next, deep learning and mixed-variable Gaussian process (GP) modeling techniques are employed to enable interpolation between microstructure families and encode meaningful patterns of variation in geometries and properties. Specifically, the latent-variable Gaussian process (LVGP) models are used to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. With this LVGP model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization.  A deep neural network model consisting of a In addition, a variational autoencoder (VAE) and a regressor for property prediction is are simultaneously trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous, and organized latent space. Our study shows several advantages of the VAE based generative model.  First,We show that the latent space of VAE provides a distance metric to measure shape similarity, enableing interpolation between microstructures and encoding encode meaningful patterns of variation in geometries and properties. 

Based on mechanistic-based learning using aforementioned machine learning models, systematic data-driven design synthesis strategies have been developed for the design of various types of metamaterial systems, including microstructure, gradient family, and multiscale systems.  While existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties, we extract critical classes of shapes from the clusters in the latent space of machine learning models, and then employ the machine learning models as the “on-the-fly” surrogate of the material law to couple the meso-scale and macro-scale topological design syntheses for efficient multiscale design optimization.